tain only positive exponents.
2) $\frac{3x^{-4}y^{-3}}{4x^{-4}y^{0}}$
4) $\frac{3x^{-2}y^{-4}}{x}$
6) $\frac{2x^{2}}{3x^{2}y^{-1} \cdot 2x^{-2}y^{4}}$
8) $\frac{4m^{-3}n^{2} \cdot 2m^{-1}n^{3}}{}$

Question

Accepted Answer

### Problem 2: Simplify $\frac{3x^{-4}y^{-3}}{4x^{-4}y^{0}}$ to contain only positive exponents.
# Explanation:
## Step 1: Simplify $x$-terms
Using the rule $\frac{a^m}{a^n}=a^{m - n}$, for $x$-terms: $x^{-4}/x^{-4}=x^{-4-(-4)} = x^{0}=1$ (since any non - zero number to the power of 0 is 1).
## Step 2: Simplify $y$-terms
For $y$-terms: $y^{-3}/y^{0}=y^{-3 - 0}=y^{-3}$. Using the rule $a^{-n}=\frac{1}{a^{n}}$, $y^{-3}=\frac{1}{y^{3}}$.
## Step 3: Simplify the constant and combine
The constant term is $3/4$. Combining with the simplified $x$ and $y$ terms, we have $\frac{3}{4}\times1\times\frac{1}{y^{3}}=\frac{3}{4y^{3}}$.
# Answer:
$\frac{3}{4y^{3}}$

### Problem 4: Simplify $\frac{3x^{-2}y^{-4}}{x}$ to contain only positive exponents.
# Explanation:
## Step 1: Simplify $x$-terms
Using the rule $\frac{a^m}{a^n}=a^{m - n}$, for $x$-terms: $x^{-2}/x^{1}=x^{-2-1}=x^{-3}$. Using $a^{-n}=\frac{1}{a^{n}}$, $x^{-3}=\frac{1}{x^{3}}$.
## Step 2: Simplify $y$-terms and combine
The $y$-term is $y^{-4}=\frac{1}{y^{4}}$ and the constant term is 3. Combining them, we get $3\times\frac{1}{x^{3}}\times\frac{1}{y^{4}}=\frac{3}{x^{3}y^{4}}$.
# Answer:
$\frac{3}{x^{3}y^{4}}$

### Problem 6: Simplify $\frac{2x^{2}}{3x^{2}y^{-1}\cdot2x^{-2}y^{4}}$ to contain only positive exponents.
# Explanation:
## Step 1: Simplify the denominator first (multiply the terms in the denominator)
For $x$-terms in the denominator: $x^{2}\cdot x^{-2}=x^{2+( - 2)}=x^{0}=1$. For $y$-terms in the denominator: $y^{-1}\cdot y^{4}=y^{-1 + 4}=y^{3}$. For the constant terms in the denominator: $3\times2 = 6$. So the denominator becomes $6\times1\times y^{3}=6y^{3}$.
## Step 2: Simplify the fraction
Now we have $\frac{2x^{2}}{6y^{3}}$. Simplify the constant fraction $2/6=\frac{1}{3}$. The $x$-term remains $x^{2}$ (since there are no $x$-terms in the denominator after simplification). So we get $\frac{x^{2}}{3y^{3}}$.
# Answer:
$\frac{x^{2}}{3y^{3}}$

### Problem 8: (Assuming the denominator is missing, but let's assume the full problem is $\frac{4m^{-3}n^{2}\cdot2m^{-1}n^{3}}{1}$ (if denominator is 1, or we can proceed with numerator first))
# Explanation:
## Step 1: Multiply the constant terms
Multiply the constant terms: $4\times2 = 8$.
## Step 2: Multiply $m$-terms
Using the rule $a^{m}\cdot a^{n}=a^{m + n}$, for $m$-terms: $m^{-3}\cdot m^{-1}=m^{-3+( - 1)}=m^{-4}$. Using $a^{-n}=\frac{1}{a^{n}}$, $m^{-4}=\frac{1}{m^{4}}$.
## Step 3: Multiply $n$-terms
For $n$-terms: $n^{2}\cdot n^{3}=n^{2 + 3}=n^{5}$.
## Step 4: Combine all terms
Combining the constant, $m$, and $n$ terms, we get $8\times\frac{1}{m^{4}}\times n^{5}=\frac{8n^{5}}{m^{4}}$.
# Answer:
$\frac{8n^{5}}{m^{4}}$ (Note: If there was a denominator, the solution would be adjusted accordingly. Since the denominator was not fully visible, this is a solution based on the visible numerator part.)

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QUESTION IMAGE

Question

Explanation:

Problem 2: Simplify \(\frac{3x^{-4}y^{-3}}{4x^{-4}y^{0}}\) to contain only positive exponents.

Step 1: Simplify \(x\)-terms

Step 2: Simplify \(y\)-terms

Step 3: Simplify the constant and combine

Step 1: Simplify \(x\)-terms

Step 2: Simplify \(y\)-terms and combine

Step 1: Simplify the denominator first (multiply the terms in the denominator)

Step 2: Simplify the fraction

Answer:

Problem 4: Simplify \(\frac{3x^{-2}y^{-4}}{x}\) to contain only positive exponents.